Schur-geometric Convexity Research Articles

Schur-power convexity of integral mean for convex functions on the coordinates

Abstract In this article, we investigate the concepts of monotonicity, Schur-geometric convexity, Schur-harmonic convexity, and Schur-power convexity for the lower and upper limits of the integral mean, focusing on convex functions on coordinate axes. Furthermore, we introduce novel and fascinating inequalities for binary means as a practical application.

Schur-Convexity for Elementary Symmetric Composite Functions and Their Inverse Problems and Applications

This paper investigates the Schur-convexity, Schur-geometric convexity, and Schur-harmonic convexity for the elementary symmetric composite function and its dual form. The inverse problems are also considered. New inequalities on special means are established by using the theory of majorization.

English

In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity on and Schur-harmonic convexity on for a composite function of the elementary symmetric functions.

Schur Geometric Convexity of Related Function for Holders Inequality with Application

In this paper, we investigated the Schur geometric convexity of related function for Holders Inequality by using majorization inequality theory and some applications are established.

Schur-Convexity for a Class of Completely Symmetric Function Dual

By using the decision theorem and properties of the Schur-convex function, the Schur-geometric convex function and the Schur-harmonic function, the Schur- convexity, Schur-geometric convexity and Schur-harmonic convexity of a class of complete symmetric functions are studied. As applications, some symmetric function inequalities are established.

Schur convexity of Bonferroni harmonic mean

In this paper, we research the Schur convexity, Schur geometric convexity and Schur harmonic convexity of the Bonferroni harmonic mean. Some inequalities identified with the Bonferroni harmonic mean are set up to represent the utilizations of the acquired outcomes.

Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities

In this paper, we discuss the Schur convexity, Schur geometric convexity and Schur harmonic convexity of the generalized geometric Bonferroni mean. Some inequalities related to the generalized geometric Bonferroni mean are established to illustrate the applications of the obtained results.

Schur-convexity for a mean of two variables with three parameters

Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a mean of two variables with three parameters are investigated, and some mean value inequalities of two variables are established.

Schur-convexity, Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function.

In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a composite function of the complete symmetric function.

Compositions involving Schur geometrically convex functions

The decision theorem of the Schur geometric convexity for the compositions involving Schur geometrically convex functions is established and used to determine the Schur geometric convexity of some symmetric functions.

Schur-geometric convexity of the generalized Gini-Heronian means involving three parameters

Abstract In this paper, we give a unified generalization of the Gini means and Heronian means. The Schur-geometric convexity of the generalized Gini-Heronian means are investigated. Our result generalizes an earlier result given by Shi et al. (J. Inequal. Appl. 2008:879273, 2008). At the end of the paper, two new inequalities related to the generalized Gini-Heronian means are established to illustrate the applicability of the given result. MSC:26D15, 26E60, 26A51.

Schur Geometric Convexity for Ratio of Difference of Means

In this paper, we study the Schur geometric convexity (concavity) of the ratio of difference of means. Also established some inter related mean inequalities related to the ratio of difference of means.

Refinements of Inequalities among Difference of Means

In this paper, for the difference of famous means discussed by Taneja in 2005, we study the Schur-geometric convexity in (0, ∞) × (0, ∞) of the difference between them. Moreover some inequalities related to the difference of those means are obtained.

Two Schur-convex functions related to Hadamard-type\\ integral inequalities

The Schur-convexity, the Schur-geometric convexity and the Schur-harmonic con- vexity of two mappings which related to Hadamard-type integral inequalities are re- searched. And three re nements of Hadamard-type integral inequality are obtained, as applications, some inequalities related to the arithmetic mean, the logarithmic mean and the power mean are established

On Schur-convexity and Schur-geometric convexity of four-parameter family of means

On Schur-convexity and Schur-geometric convexity of four-parameter family of means

Schur-convexity and Schur-geometrically concavity of Gini means

The Schur-convexity and the Schur-geometric convexity with variables ( x , y ) ∈ R + + 2 for fixed ( s , t ) of Gini means G ( r , s ; x , y ) are discussed. Some new inequalities are obtained.

Schur Convexity of Generalized Heronian Means Involving Two Parameters

The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two parameters are studied, the main result is then used to obtain several interesting and significantly inequalities for generalized Heronian means.

A class of symmetric functions for multiplicatively convex function

A new symmetric function, which generalizes Hamy symmetric function, is defined. Its properties, including Schur-geometric convexity, are investigated. Some analytic inequalities are also established. Mathematics subject classification (2000): 26A51, 26D15, 0E05.